Newton’s Laws of Motion

How and why objects move as they do has fascinated scientists for thousands of years. In the early 1600s, the Italian astronomer Galileo Galilei suggested that, once an object is in motion, no force is needed to keep it moving. Force is needed only to change the motion of an object. Galileo's ideas paved the way for Isaac Newton. Newton proposed the three basic laws of motion in the late 1600s.

The First Law of Motion Newton’s first law restates Galileo's ideas about force and motion. Newton’s first law of motion states that an object at rest will remain at rest, and an object moving at a constant velocity will continue moving at a constant velocity , unless it is acted upon by an unbalanced force.

If an object is not moving, it will not move until a force acts on it. Clothes on the floor of your room will stay there unless you pick them up. If an object is already moving, it will continue to move at a constant velocity until a force acts to change either its speed or direction.

For example, a tennis ball flies through the air once you hit it with a racket. If your friend doesn’t hit the ball back, the forces of gravity and friction will eventually stop the ball. On Earth, gravity and friction are unbalanced forces that often change an object’s motion.

Inertia Whether an object is moving or not, it resists any change to its motion. Galileo’s concept of the resistance to a change in motion is called inertia. Inertia is the tendency of an object to resist a change in motion. Newton’s first law of motion is called the law of inertia.

Inertia explains many common events, such as why you move forward in your seat when a car stops suddenly. When the car stops, inertia keeps you moving forward. A force, such as the pull of a seat belt, is required to change your motion.

Some objects have more inertia than other objects. For example, suppose you needed to move an empty aquarium and an aquarium full of water. Obviously, the full aquarium is harder to move than the empty one, because it has more mass. The greater the mass of an object, the greater its inertia, and the greater the force required to change its motion. The full aquarium is more difficult to move because it has more inertia than the empty aquarium.

The Second Law of Motion Suppose you are baby-sitting two children who love wagon rides. Their favorite part is when you accelerate quickly. When you get tired and sit in the wagon, one of the children pulls you. He soon finds he cannot accelerate the wagon nearly as fast as you can. How is the wagon’s acceleration related to the force pulling it?

How is the acceleration related to the wagon’s mass? According to Newton’s second law of motion, acceleration depends on the object’s mass and on the net force acting on the object. This relationship can be written as an equation: Acceleration = Net Force/ Mass

Acceleration is measured in meters per second per second (m/s2), and mass is measured in kilograms (kg). According to Newton’s second law, then, force is measured in kilograms times meters per second per second (kg x m/s2). The short for this unit of force is the newton (N). Recall that a newton is the metric unit of force. You can think of one newton as the force required to give a 1-kg mass an acceleration of 1 m/s2.

Sample Problem A speedboat pulls a 55 kg water skier. The force causes the skier to accelerate at 2.0 m/s2. Calculate the net force that causes this acceleration. What information are you given? Mass of water skier = 55 kg Acceleration of the water skier = 2.0 m/s2

What quantity are you trying to calculate? The net force What formula will you use? Acceleration = Net force ÷ mass OR Net Force = mass x acceleration Perform the calculation Fnet = m x a F = 55 kg x 2.0 m/s2 F = 110 kg x m/s2 F = 110 N

Practice Problems What is the net force on a 1,000 kg object accelerating at 3 m/s2? What net force is needed to accelerate a 25 kg cart at 14 m/s2?

Changes in Force and Mass How can you increase the acceleration of the wagon? Look again at the equation. One way to increase acceleration is by changing the force. If the mass is constant, acceleration and force change in the same way. So to increase the acceleration of the wagon, you can increase the force used to pull it.

Another way to increase acceleration is to change the mass. According to the equation, acceleration and mass change in opposite ways. If the force is constant, an increase in mass causes a decrease in acceleration. The opposite is also true: A decrease in mass causes an increase in acceleration with a constant force. To increase the acceleration of the wagon, you can decrease its mass. So instead of you, the children should ride in the wagon.

Look at the pictures on the right. Which vehicle do you think would require a greater force to push? Why do you think this? Using the equation, solve for the amount of force.

Newton’s Third Law of Motion Newton proposed that whenever one object exerts a force on a second object, the second object exerts a force back on the first object. The force exerted by the second object is equal in strength and opposite in direction to the first force. Think of one force as the “action” and the other force as the “reaction.”

Newton’s third law of motion states that if one object exerts a force on another object, then the second object exerts a force of equal strength in the opposite direction on the first object. Another way to state Newton’s third law is that for every action there is an equal but opposite reaction.

Action-Reaction Pairs You’re probably familiar with many examples of Newton’s third law. Pairs of action and reaction forces are all around you. When you jump, you push on the ground with your feet. This is the action force. The ground pushes back on your feet with an equal and opposite force. This is the reaction force.

You move upward when you jump because the ground is pushing you! In a similar way, a kayaker moves forward by exerting an action force on the water with a paddle. The water pushes back on the paddle with an equal reaction force that propels the kayak forward. Now you can understand what happens when you teach your friend how to rollerblade. Your friend exerts an action force when he pushes against you to start. You exert a reaction force in the opposite direction. As a result, both of you move in opposite directions.

Figure 15Action-Reaction Pairs Action-reaction pairs explain how a gymnast can flip over a vaulting horse, how a kayaker can move through the water, and how a dog can leap off the ground. Observing Name some other action-reaction pairs that you have observed.

Detecting Motion Can you always detect motion when paired forces are in action? The answer is no. For example, when Earth’s gravity pulls on an object, you cannot detect Earth’s equal and opposite reaction. Suppose you drop your pencil. Gravity pulls the pencil downward.

At the same time, the pencil pulls Earth upward with an equal and opposite reaction force. You don’t see Earth accelerate toward the pencil because Earth’s inertia is so great that its acceleration is too small to notice.

Do Action-Reaction Forces Cancel? Earlier you learned that if two equal forces act in opposite directions on an object, the forces are balanced. Because the two forces add up to zero, they cancel each other out and produce no change in motion. Why then don’t the action and reaction force in Newton’s third law of motion cancel out as well? After all, they are equal and opposite.

The action and reaction forces do not cancel out because they are acting on different objects. Look at the volleyball player on the left in Figure 16. She exerts an upward action force on the ball. In return, the ball exerts an equal but opposite downward reaction force back on her wrists. The action and reaction forces act on different objects.

On the other hand, the volleyball players on the right are both exerting a force on the same object – the volleyball. When they hit the ball from opposite directions, each of their hands exerts a force on the ball equal in strength but opposite in direction. The forces on the volleyball are balanced and the ball does not move either to the left or to the right.

How fast will an 800kg car accelerate if it is pushed with 4000N of force? How fast will a 0.15kg hockey puck accelerate if it is hit with 1.2 N of force?